This paper proposes a Schur complement-based Domain Decomposition Method to accelerate the time-domain simulation of large, non-linear and stiff Differential and Algebraic Equation systems stemming from power system dynamic studies. The proposed algorithm employs a star-shaped decomposition scheme and exploits the locality and sparsity of the system. The simulation is accelerated by the use of quasi-Newton schemes and parallel programming techniques. The proposed algorithm is implemented using the shared-memory parallel programming model and tested on a large-scale, realistic power system model showing significant speedup.